2-Normlu Büyük Dizi Uzayları Üzerine Bir Not

Year 2022, , 269 - 273, 15.06.2022

Oğuz Oğur

https://doi.org/10.31466/kfbd.1031895

Abstract

Bu çalışmada, (Gunawan, 2001) ve (Rafeiro et. al., 2018) çalışmalarindan esinlenerek 2-normlu büyük dizi uzaylarını tanımladık. Ayrıca, bu uzayların bazı temel özelliklerini verdik.

Keywords

Büyük dizi uzayları, 2-normlu uzaylar, Lebesgue dizi uzayları.

A Note on 2-Normed Grand Sequence Spaces

Abstract

In this paper, we define 2-normed grand sequence space by inspiration of (Gunawan, 2001) and (Rafeiro et. al., 2018). Also, we give some basic properties of these spaces.

Keywords

Grand sequence space, 2-normed space, Lebesgue sequence space.

References

• Duyar, C., Kanber, O. and Sağır, B., (2016). On n-normed Cesaro sequence space Cesn,p. Int. Electron. J. Pure Appl. Math., 10(2): 151-159.
• Duyar, C., Sağır, B. and Oğur, O., (2017). On a class of n-normed double sequences related to p-summable double sequence space l_p^((2)). E. J. Mathematical Anal. App., 5(1): 106-111.
• Gahler, S., (1964). Lineare 2-normierte Raume, Math. Nachr., 28: 1-43.
• Gunawan, H., (2001). The space of p-summable sequences and its natural n-norm. Bull. Austral. Math. Soc., 64, 137-147.
• Iwaniec, T. and Sbordone, C., (1992). On the integrability of the Jacobian under minimal hypotheses, Arch. Ration. Mech. Anal., 119(2), 129-143.
• Jain, P. and Kumari, S., 2010. On grand Lorentz spaces and the maximal operator, Math. Student, 79.
• Oğur, O., (2018). Superposition operator on some 2-normed sequence spaces. Karaelmas Science and Engineering journal, 8(1), 288-291.
• Oğur, O., (2020). Grand Lorentz sequence space and its multiplication operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics , 69 (1) , 771-781.
• Rafeiro, H., Samko, S. and Umarkhadzhiev, S., (2018). Grand Lebesgue sequence spaces. Georgian Math. J., 19(2), 235-246.
• Samko, S. and Umarkhadzhiev, S., (2017), On grand Lebesgue spaces on sets of infinite measure, Math. Nachr., 290, 913-919.
• Swe, T. T., (2019). Bounded linear 2-functionals in linear 2-normed space. Dagon University Commemoration of 25. Anniversary Silver Jubilee Research Journal, 9, 203.